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Homework 3 is due Tuesday, February 16. See Homework link.

Causality and Determinism

· Hume. Causation is a misguided mental construct

· Kant . Causation is established by pure reason alone and inextricable from any sensible view of the physical world.

· Lewis . Causation is established by counterfactual dependency.

· Counterfactuals and free will . Free will is simply the ability to do otherwise. This statement is best understood as the existence of a possible world in which one did otherwise. Each world can be purely deterministic but as long there is no logical inconsistency with the existence of other possible worlds, then the ability to do otherwise exists.

· Free Will and determinism: Hume . While most saw free will and determinism as being incompatible, Hume saw free will and indeterminism as being incompatible. His argument is as follows. Let's assume that one's actions are not determined by any prior events. Hence, your actions are not determined by your character, preferences, wishes, desires, etc. That is, your actions are random. Then the question arises, how can we hold someone responsible if their actions are not determined by their character. Hence for Hume, free will entails determinism; human behaviour arises from a causal chain. It is not random. There must be some causal connection linking your actions to your desires for their to be anything such as moral responsibility. Desires are shaped in part by one's history. For Hume, free will is to be understood on the counterfactual account as the hypothetical ability to do otherwise. Since there is nothing necessary about desires and preferences, there is no logical problem to entertain the possibility that things could have been otherwise. Hume's view goes under another name: compatibilism.

· Moral responsibility and determinism: Harry G. Frankfurt (author of recently published monogram entitled, ``On Bullshit'') . It is generally assumed that one has to be able to do otherwise for one to be held morally responsible (however one wants to define that) for one's actions. This is the principle of alternative possibilities (PAP). John Frankfurt established a set of counterexamples to this from which it became clear that determinism and moral responsibility are not necessarily incompatible. Let's take two indidviduals, Jones and Homer. Jones deliberates and ponders the possibility of stealing a VCR from Best Buy. Let's assume he does not own Best Buy. Hence, it would be stealing if he goes through with his actions. Let's say after much deliberation he decides to steal the VCR. Now let's introduce Homer, an individual who has the power and the intention to make Jones do whatever he wants. But Homer holds his cards close to his chest and only intervenes when he has to change the course of Jones's actions. By coincidence, Homer wants Jones to steal the VCR. And hence Homer does not have to intervene. Because Jones deliberates and does what he wants without any intervention, Jones is morally responsible for stealing the VCR. However, there is only one output in this deterministic system. Namely, Jones must steal the VCR. Hence, we have a perfectly deterministic system (in this instance) but Jones is morally responsible. Are there any loopholes in this argument? This example comes from a long line of examples of this sort known as Frankfurt examples. The key point this example illustrates is that someone does not need to be able to do otherwise to be morally responsible.

Other conserved quantities (not known by Newton):

· Energy. Energy is more complicated, because it has many apparently dissimilar forms. Its conservation was not clearly understood until the 19^th century. (More below)

· Electric charge. This law was discovered by Faraday, also in the 19^th century.

Energy

Energy conservation is more difficult to observe than momentum, because energy can exist in various subtle forms. (So can momentum, but in many cases momentum stays in the form of nice visible motions.)

There's

1. kinetic energy (mv²/2)

2. potential energy (depends on positions of objects with forces between them, e.g. -GM₁M₂/r₁₂ for gravity)

3. chemical energy, "heat",

The history of heat illustrates how the interpretation of data is colored by one’s theoretical framework. In the 18th century, heat was thought to be a fluid, the caloric. Lavoisier The temperature of an object depended on the amount of caloric it contained, like the height of water in a container depends on the amount of fluid it contains. Just as water flows from higher to lower, heat would flow from hotter to colder regions.

Count Rumford’s cannon-boring experiment (1798) was the first blow against the caloric theory. Rumford rubbed a blunt tool used to bore a cannon against a flat plate. He then placed the plate and tool in a beaker of water. After a while, the water boiled. Since the only items Rumford transferred to the beaker were the tool and the plate, the boiling of the water must have occured from these items alone. Hence, we have an instance of heating without a caloric. Rumford reasoned that heat must be nothing more than motion. In fact, a fairly good definition of energy is: motion that is entirely convertible into heat and hence a temperature increase or decrease. Notice, on this definition, energy provides a qualitatively different measure of motion than does the momentum. The momentum is mass*velocity. A particle that is moving back and forth in a straight line has no net momentum because the forward and backward momenta exactly cancel. However, such a particle has energy because the energy goes as the square of the velocity.

Newtonian cosmology:

The universe must be infinite for several reasons:

• A finite one would ‘run down’ due to friction (e.g., tides).

• A finite one has a center (i.e., absolute position).

• Hard to reconcile Euclidean geometry with a finite universe.

However, an infinite universe has at least two problems:

Olber’s paradox:

In an infinite, homogeneous (that is, uniform density) universe that is unchanging in time, then regardless of where one looks in the sky, one should eventually see a star albeit far out. Hence, there should be no dark spots in the sky. Dark spots indicate that part of the sky is cold. Why such drastic temperature gradients persist between bright objects and dark objects is the question? Mathematically, this paradox can be stated as follows. Consider a shell in the sky of radius R and width W. The flux energy from one star is f=L/(4\pi R^2). Let n be the density of stars in the volume carved out by the shell. The number of stars in the volume is N=n 4 pi R^2 W. The total luminosity from the stars in the shell is F=Nf=nLW, a number independent of the distance the stars are from us. This means that all shells we can slice the sky in should be equally bright. So lets take lots of slices. We should see brightness everywhere. But we do not. This suggests that the world is in a state of disequilibrium. Note saying that there is dust in the dark regions does not work. Dust will heat up and radiate energy. So there should be radiation in the dark regions. But the dark regions are cold. So this does not work.

There may be ways around this problem (e.g.: 1) the stars stop beyond some point, or 2) we are experiencing a 1 chance in 10^10^80 year disequilbrium in the universe. Neither of these is acceptable, however. SIZE=5>:

The answer lies in the assumption of a static universe. Understanding what force regulates the grand cosmic motion is the big unaswered question.

^† Actually, dust doesn’t work either in an infinitely old universe. The dust would just heat up and glow like a star.
Can the universe be infinitely old? What about the finite stellar lifetime, from conservation of energy?

Conclusions on Newton

Gravity

Explanation of Kepler's laws

Symmetry and Invariance

Inertia is problemetic: Absolute space